• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.571-575
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• 2002

In this paper we show that Weyl's theorem holds for f(T) when an Hilbert space operator T is “algebraically totally-paranormal” and f is any analytic function on an open neighbor-hood of the spectrum of T.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.75-82
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• 2003

In this note it is shown that if T satisfies ($G_{1}$)-condition with finite spectrum then Weyl's theorem holds for T. If T is totally *-paranormal then $T-{\lambda}$ has finite ascent for all ${\lambda}{\in}{\mathbb{C}},\;T$ is isoloid, and Weyl's theorem holds for T.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.53-64
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• 2006

In this paper, we are concerned with the algebraic representation of the quasi-nilpotent part for prehermitian operators on Banach spaces. The quasi-nilpotent part of an operator plays a significant role in the spectral theory and Fredholm theory of operators on Banach spaces. Properties of the quasi-nilpotent part are investigated and an application is given to totally paranormal and prehermitian operators.